“Thee” and “thou” in “The Lord of the Rings”

[The Might]

Actually Galadriel, he does in the Unfinished Tales:

She did not seek to comfort him any more than herself: for she met her grief in silence and coldness of heart. But Húrin mourned openly, and he took up his harp and would make a song of lamentation; but he could not, and he broke his harp, and going out he lifted up his hand towards the North, crying: "Marrer of Middle-earth, would that I might see thee face to face, and mar thee as my lord Fingolfin did!"

Also, interesting to note that both Turin and Gurthang(!) use "thee" in their short dialogue:

"Hail Gurthang, iron of death, thou alone now remainest! But what lord or loy*alty dost thou know, save the hand that wieldeth thee? From no blood wilt thou shrink! Wilt thou take Túrin Turambar? Wilt thou slay me swiftly?"
And from the blade rang a cold voice in answer: "Yea, I will drink thy blood, that I may forget the blood of Beleg my master, and the blood of Brandir slain unjustly. I will slay thee swiftly."